(x+3)(2x-5)=(x+3)(x+7)

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Solution for (x+3)(2x-5)=(x+3)(x+7) equation: 


Simplifying
(x + 3)(2x + -5) = (x + 3)(x + 7)

Reorder the terms:
(3 + x)(2x + -5) = (x + 3)(x + 7)

Reorder the terms:
(3 + x)(-5 + 2x) = (x + 3)(x + 7)

Multiply (3 + x) * (-5 + 2x)
(3(-5 + 2x) + x(-5 + 2x)) = (x + 3)(x + 7)
((-5 * 3 + 2x * 3) + x(-5 + 2x)) = (x + 3)(x + 7)
((-15 + 6x) + x(-5 + 2x)) = (x + 3)(x + 7)
(-15 + 6x + (-5 * x + 2x * x)) = (x + 3)(x + 7)
(-15 + 6x + (-5x + 2x2)) = (x + 3)(x + 7)

Combine like terms: 6x + -5x = 1x
(-15 + 1x + 2x2) = (x + 3)(x + 7)

Reorder the terms:
-15 + 1x + 2x2 = (3 + x)(x + 7)

Reorder the terms:
-15 + 1x + 2x2 = (3 + x)(7 + x)

Multiply (3 + x) * (7 + x)
-15 + 1x + 2x2 = (3(7 + x) + x(7 + x))
-15 + 1x + 2x2 = ((7 * 3 + x * 3) + x(7 + x))
-15 + 1x + 2x2 = ((21 + 3x) + x(7 + x))
-15 + 1x + 2x2 = (21 + 3x + (7 * x + x * x))
-15 + 1x + 2x2 = (21 + 3x + (7x + x2))

Combine like terms: 3x + 7x = 10x
-15 + 1x + 2x2 = (21 + 10x + x2)

Solving
-15 + 1x + 2x2 = 21 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-15 + -21 + 1x + -10x + 2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: -15 + -21 = -36
-36 + 1x + -10x + 2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: 1x + -10x = -9x
-36 + -9x + 2x2 + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-36 + -9x + 1x2 = 21 + 10x + x2 + -21 + -10x + -1x2

Reorder the terms:
-36 + -9x + 1x2 = 21 + -21 + 10x + -10x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-36 + -9x + 1x2 = 0 + 10x + -10x + x2 + -1x2
-36 + -9x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-36 + -9x + 1x2 = 0 + x2 + -1x2
-36 + -9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -9x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-3, 12}

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